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The Regulation of Cellular Systems
TLDR
The basic equations of metabolic control analysis are rewritten in terms of co-response coefficients and internal response coefficients to describe the interaction of optimization methods and the interrelation with evolution.Abstract:
Introduction Fundamentals of biochemical modeling Balance equations Rate laws Generalized mass-action kinetics Various enzyme kinetic rate laws Thermodynamic flow-force relationships Power-law approximation Steady states of biochemical networks General considerations Stable and unstable steady states Multiple steady states Metabolic oscillations Background Mathematical conditions for oscillations Glycolytic oscillations Models of intracellular calcium oscillations A simple three-variable model with only monomolecular and bimolecular reactions Possible physiological significance of oscillations Stoichiometric analysis Conservation relations Linear dependencies between the rows of the stoichiometry matrix Non-negative flux vectors Elementary flux modes Thermodynamic aspects A generalized Wegscheider condition Strictly detailed balanced subnetworks Onsager's reciprocity reactions for coupled enyme reactions Time hierarchy in metabolism Time constants The quasi-steady-state approximation The Rapid equilibrium approximation Modal analysis Metabolic control analysis Basic definitions A systematic approach Theorems of metabolic control analysis Summation theorems Connectivity theorems Calculation of control coefficients using the theorems Geometrical interpretation Control analysis of various systems General remarks Elasticity coefficients for specific rate laws Control coefficients for simple hypothetical pathways Unbranched chains A branched system Control of erythrocyte energy metabolism The reaction system Basic model Interplay of ATP production and ATP consumption Glycolytic energy metabolism and osmotic states A simple model of oxidative phosphorylation A three-step model of serine biosynthesis Time-dependent control coefficients Are control coefficients always parameter independent? Posing the problem A system without conserved moieties A system with a conserved moiety A system including dynamic channeling Normalized versus non-normalized coefficients Analysis in terms of variables other than steady-state concentrations and fluxes General analysis Concentration ratios and free-energy-differences as state variables Entropy production as response variable Control of transient times Control of oscillations A second-order approach A quantitative approach to metabolic regulations Co-response coefficients Fluctuations of internal variables versus parameter perturbations Internal response coefficients Rephrasing the basic equations of metabolic control analysis in terms of co-response coefficients and internal response coefficients Control within and between subsystems Modular approach Overall elasticities Overall control coefficients Flux control insusceptibility Control exerted by elementary steps in enzyme catalysis Control analysis of metabolic channeling Comparison of metabolic control analysis and power-law formalism Computational aspects Application of optimization methods and the interrelation with evolution Optimization of the catalytic properties of single enzymes Basic assumptions Optimal values of elementary rate constants Optimal Michaelis constants Optimization of multienzyme systems Maximization of steady-state flux Influence of osmotic constraints and minimization of intermediate concentrations Minimization of transient times Optimal stoichiometries.read more
Citations
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Robustness Analysis, Prediction and Estimation for Uncertain Biochemical Networks
Stefan Streif,Stefan Streif,Kwang-Ki K. Kim,Philipp Rumschinski,Philipp Rumschinski,Masako Kishida,Dongying Erin Shen,Rolf Findeisen,Richard D. Braatz +8 more
TL;DR: Network functions and behaviors of interest are formally defined, and different classes of uncertainties and perturbations in the data and model are consistently described, and the capabilities of frequently used approaches are illustrated.
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Application of Lumping Analysis in Modelling the Living Systems - A Trade-off Between Simplicity and Model Quality
TL;DR: Derivation of a satisfactory model is closely related to the ability of selecting the suitable lumping rules, key-parameters, and influential terms that better realize a trade-off between model simplicity and its predictive quality.
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ALC: automated reduction of rule-based models
TL;DR: ALC allows for a simple rule-based generation of layer-based reduced models that show a pronounced modularity in the simulation equations.
Journal ArticleDOI
Thresholds in transient dynamics of signal transduction pathways
TL;DR: This work focuses on the identification of thresholds that separate different transient dynamic behaviors, and finds the spectrum of the finite-time Lyapunov exponents unambiguously and reliably identifies putative thresholds in transient dynamics.
Journal ArticleDOI
Simplification and its consequences in biological modelling: conclusions from a study of calcium oscillations in hepatocytes
TL;DR: In this paper, a collection of models is constructed, each a progressively more simplified version of a well-understood model, each one is a piecewise linear model that can be solved analytically.
References
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Book
Linear Multivariable Control: A Geometric Approach
TL;DR: In this article, the authors present an approach to controlability, feedback assignment, and pole shifting in a single linear functional model, where the observer is assumed to be a dynamic observer.